A waveguide is a material medium that confines and guides a propagating electromagnetic wave. An optical waveguide may comprise a filament of a light conducting medium, where the light conducting medium may include silicon dioxide (SiO2), silicon, compound semiconductors, etc. The filament of the light conducting medium may be referred to as a core, and the core may be surrounded by a cladding. The cross section of the optical waveguide may be circular or rectangular. The refractive index of the core is higher than that of the cladding for the light to be guided by the optical fiber.
An arrayed waveguide grating may be comprised of circuitry in which optical waveguides comprising a silica-based cladding and core are fabricated on a substrate of silicon. Crosstalk may affect the performance characteristics of an arrayed waveguide grating. Optical phase errors in the waveguides that comprise the arrayed waveguide grating may contribute to the crosstalk. The optical phase error in a waveguide, ∂ø, may be caused by imperfections in the waveguide as a result of fabrication processes. The imperfections may be caused by fluctuations in waveguide parameters, such as, the spatial core size error, ∂w, the refractive index error of the core, ∂n core, the refractive index error of the cladding, ∂nclad, and the actual waveguide length error, ∂L.
The ability to identify and extract the optical phase errors in a waveguide may assist in debugging the design of waveguides and in improving the fabrication process of waveguides. The optical performance of arrayed waveguide gratings and other devices, such as, devices based on Mach-Zehnder interferometers, may also be improved, where the performance of the arrayed waveguide gratings and the other devices are affected by the optical phase errors of waveguides.
Details of the theory of waveguides are described in the book “Integrated Optics: Design and Modeling” by Reinhard Marz, published by Artech House, Inc., 1995. Certain techniques for extracting optical phase errors in waveguides and interferometers are described in the publication entitled “Estimation of Waveguide Phase Error in Silica-Based Wavelengths” by T. Goh, S. Suzuki, and A. Sugita, published in the Journal of Lightwave Technology, Vol. 15, No. 11, November 1997, pages 2107–2113.